Fwd: Re: [CF-metadata] ungridded data

From: Bob Drach <drach>
Date: Mon, 24 Jun 2002 16:46:18 -0700

Dear Jonathan,

> I think you are setting yourself a hard task to distinguish such a tiling of
> the whole surface from an irregular set of scattered points.

I'm really trying to pin down the definition of 'grid' in a sense that will be
useful to application writers. It is certainly difficult, but given that the term
is used frequently in CF I hope the effort is worth it.

> This is getting
> outside the bounds of a purely technical question into the area of scientific
> interpretation. Structurally the two are identical because functionally they
> are really quite similar. For example, suppose you have a reduced grid covering
> the whole Earth i.e. no gaps between its boxes. Then omit a single gridbox. Is
> this now a reduced grid with a box missing, or is it a set of scattered points
> each with an associated box surrounding it? Or, starting from the other end, it
> might be the case that a small set of scattered station data spread over the
> world really might be being used to estimate a global average quantity. Sea
> level change is estimated from tide gauges in this kind of way. In this
> case the user would actually or notionally have associated some kind of
> region with each station, so it is not obvious that it would be inappropriate
> to guess at the gridbox boundaries.
>
> However, the grid_mapping attribute we have been discussing may help. I suppose
> that if there is a grid_mapping, it means that the whole world (or the portion
> of it being considered) has been systematically covered in some kind of way.
> The application may not understand how the grid_mapping works, but perhaps the
> presence of this attribute would be sufficient to decide that the data was a
> set of boxes covering the surface, rather than a set of irregularly scattered
> points.

Part of the question is whether there are any georeferenced data in CF that are
not gridded (!). My sense is that the notion of'irregularly scattered points' lies
outside the range of what is commonly called gridded, but that data with an
associated tiling, or nonoverlapping convex cells (gridboxes) - particularly if
the tiling covers the surface - could reasonably be called gridded. A tiling that
covers a contiguous region carries the added notion of connectivity. But I agree
with Brian that you can have a grid without explicitly defined gridboxes, e.g.,
the example of spectral data translated to a T42 grid.

Let me try to distill the discussion into a working definition of horizontal grid:

Conceptually, a horizontal grid represents a discretization and
structuring/ordering of lat-lon space. More formally, a (horizontal) grid is the
discretization of a 1-1 mapping from a two-dimensional index space into lat-lon
space. A grid may or may not have associated boundary information, representing
the decomposition of lat-lon space into nonoverlapping cells, such that each point
of the grid is contained in the corresponding cell.

If in addition to being 1-1 the grid mapping function is a discretization of a
continuous function, then the grid is considered to carry connectivity
information, in the sense that for a given i,j, the neighboring grid points of
point (i,j) are (i+/-1,j) and (i,j+/-1). Similarly, if boundary information is
specified, and cells P, Q share an edge, then their corresponding grid points are
neighbors.

In CF the grid information is represented by coordinate variables and/or auxiliary
coordinate variables [and/or a grid_mapping definition?], and the optional
boundary information by boundary variables associated with the coordinate
variables. CF stipulates the representation for three types of horizontal grids:
independent lat/lon coordinate variables, dependent lat/lon coordinate variables,
and reduced grids:

Independent lat-lon variables: The grid mapping g(i,j) == <lat(i,j), lon(i,j)> is
represented by g(i,j) = <lat(i), lon(j)>. The stronger definition of grid applies
here, reflected in the requirement that lat and lon are monotonic. It is in this
sense that a grid mapping imposes an ordering.

Dependent lat-lon variables: g(i,j) = <lat(i,j), lon(i,j)> such that g is 1-1. The
stronger sense of continuity applies to this case.

Reduced grid: g(i,j) = <lat(i), lon(i,j)> such that g is 1-1, and lat(i) is
monotonic.



Best regards,

Bob
Received on Mon Jun 24 2002 - 17:46:18 BST